Spectral efficiency is the key factor for the development of future wireless communications. Orthogonal Frequency Division Multiple Access (OFDMA) is the multiple access technology used at physical layer of latest wireless communication technologies. Anything on the improvement or overcoming the disadvantage of the present system will be considered for the future wireless systems. Long Term Evolution (LTE) is one of the 4th generation wireless communications and it is taken as the reference system in this thesis. The main concern of this thesis is to analyze the LTE radio frame. We designed and simulated the OFDM system with cyclic prefix, its Bit Error Rate (BER) is verified by changing the Signal to Noise Ratio (SNR) value and we investigated the OFDM system by eliminating the cyclic prefix. By eliminating cyclic prefix bandwidth efficiency is achieved, though using cyclic prefix in OFDM has more advantages. Filter banks are used to compensate the advantages of cyclic prefix when it is removed. Introducing Offset in QAM results in less distortion and amplitude fluctuations. We designed, simulated and compared the QAM digital modulation with Offset-QAM digital modulation its BER vs. SNR are verified using simulations on MATLAB.